Guo Xiao, Zhang Chunming
Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China.
Department of Statistics, University of Wisconsin-Madison, Madison, WI 53706, USA.
Entropy (Basel). 2018 Mar 5;20(3):168. doi: 10.3390/e20030168.
An important issue for robust inference is to examine the stability of the asymptotic level and power of the test statistic in the presence of contaminated data. Most existing results are derived in finite-dimensional settings with some particular choices of loss functions. This paper re-examines this issue by allowing for a diverging number of parameters combined with a broader array of robust error measures, called " ", for the class of "general linear models". Under regularity conditions, we derive the influence function of the parameter estimator and demonstrate that the Wald-type test enjoys the robustness of validity and efficiency asymptotically. Specifically, the asymptotic level of the test is stable under a small amount of contamination of the null hypothesis, whereas the asymptotic power is large enough under a contaminated distribution in a neighborhood of the contiguous alternatives, thus lending supports to the utility of the proposed Wald-type test.
稳健推断的一个重要问题是，在存在污染数据的情况下，检验统计量的渐近水平和功效的稳定性。大多数现有结果是在有限维设定下，通过对损失函数的一些特定选择得出的。本文通过考虑参数数量发散，并结合更广泛的稳健误差度量（称为“ ”），对“一般线性模型”类重新审视了这个问题。在正则条件下，我们推导了参数估计量的影响函数，并证明了 Wald 型检验渐近地具有有效性和效率的稳健性。具体而言，在原假设少量污染的情况下，检验的渐近水平是稳定的，而在邻接备择假设附近的污染分布下，渐近功效足够大，从而支持了所提出的 Wald 型检验的实用性。
